Wierd problem in 88 GT

[Hammer]

Never seen this before, but maybe you guys have...

Turn on the ignition, all the self-test dash lights come on as normal... wait 5 to 7 seconds, the power resets (flickers out) for about a quarter to half a second and comes back on. Start the car, it'll fire up fine, but about 3 seconds later it'll die as my dash warning lights flicker. Fire it up again... same thing. I can keep it going through the "hiccup" by keeping the throttle down a bit. Funny thing is, once it's going for about 60 seconds.... it runs without a problem.
Get to the store, buy your groceries, get back in the car... same problem.

the exterior\interior\backlit dash lights are not effected. From what I can tell maybe its something with the computer since the instrument warning lights as well as the ignition seem to be affected? A common ground somewhere?

Thanks for any help you can give...